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Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.


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Proceedings ArticleDOI
19 Apr 1994
TL;DR: The interesting case, for applications, of using an ordinary VQ codebook as encoder, together with the soft decision decoder, gives comparable performance to channel optimized VQ with hard decisions.
Abstract: A soft decision decoder is presented. The soft decision decoder is optimal in the mean square sense, if the encoder entropy is full. A source vector estimate is obtained as a linear mapping of a soft Hadamard column. The soft Hadamard column is formed as a generally nonlinear mapping of soft information bits. It is shown that the best index assignment, on the encoder, is obtained in the special case of a linear mapping from the soft information bits. Simulations indicate that the jointly trained system performs better than channel optimized VQ with hard decisions. The interesting case, for applications, of using an ordinary VQ codebook as encoder, together with our soft decision decoder, is also investigated. In our examples this approach gives comparable performance to channel optimized VQ with hard decisions. >

38 citations

Journal ArticleDOI
TL;DR: In this paper, an extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes, and is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations.

38 citations

Journal ArticleDOI
TL;DR: A general method unifying the known constructions of binary self-orthogonal codes from designs is described, finding more than 70 inequivalent extremal doubly even self-dual codes of length 40 constructed from Hadamard matrices of order 20.

38 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the symmetry of the off-diagonal heat-kernel coefficients and the coefficients corresponding to the short distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds can be obtained by approximating C∞ metrics with analytic metrics in common geodesically convex neighborhoods.
Abstract: We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds. The requirement of such a symmetry played a central role in the theory of the point-splitting one-loop renormalization of the stress tensor in either Riemannian or Lorentzian manifolds. Actually, the symmetry of these coefficients has been assumed as a hypothesis in several papers concerning these issues without an explicit proof. The difficulty of a direct proof is related to the fact that the considered off-diagonal heat-kernel expansion, also in the Riemannian case, in principle, may be not a proper asymptotic expansion. On the other hand, direct computations of the off-diagonal heat-kernel coefficients are impossibly difficult in nontrivial cases and thus no case is known in the literature where the symmetry does not hold. By approximating C∞ metrics with analytic metrics in common (totally normal) geodesically convex neighborhoods, it is rigorously proven that in general C∞ Riemannian manifolds, any point admits a geodesically convex neighborhood where the off-diagonal heat-kernel coefficients, as well as the relevant Hadamard expansion coefficients, are symmetric functions of the two arguments.

38 citations

Journal ArticleDOI
TL;DR: The authors' numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the discrete-time quantum walk with on-site static/dynamic phase disorder.
Abstract: Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.

38 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023339
2022850
2021391
2020444
2019427
2018372